Star product representation of coherent state path integrals

TL;DR

This paper develops a star product framework for coherent state path integrals, connecting phase space representations with quantum dynamics through generalized delta functions and star exponentials.

Contribution

It introduces a novel star product representation of coherent path integrals and relates them to phase space functions like the P and Q representations.

Findings

Derived the star product form of the coherent state path integral.

Expressed the time evolution operator in terms of the Q-representation and star product.

Established the coherent state path integral as a star exponential of the Hamiltonian.

Abstract

In this paper, we determine the star product representation of coherent path integrals. By employing the properties of generalized delta functions with complex arguments, the Glauber-Sudarshan P-function corresponding to a non-diagonal density operator is obtained. Then, we compute the Husimi-Kano Q-representation of the time evolution operator in terms of the normal star product. Finally, the optical equivalence theorem allows us to express the coherent state path integral as a star exponential of the Hamiltonian function for the normal product.